Problem: Ben is 3 times as old as Nadia. Twenty years ago, Ben was 8 times as old as Nadia. How old is Ben now?
We can use the given information to write down two equations that describe the ages of Ben and Nadia. Let Ben's current age be $b$ and Nadia's current age be $n$ The information in the first sentence can be expressed in the following equation: $b = 3n$ Twenty years ago, Ben was $b - 20$ years old, and Nadia was $n - 20$ years old. The information in the second sentence can be expressed in the following equation: $b - 20 = 8(n - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $n$ and substitute it into our second equation. Solving our first equation for $n$ , we get: $n = b / 3$ . Substituting this into our second equation, we get: $b - 20 = 8($ $(b / 3)$ $- 20)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 20 = \dfrac{8}{3} b - 160$ Solving for $b$ , we get: $\dfrac{5}{3} b = 140$ $b = \dfrac{3}{5} \cdot 140 = 84$.